Regular Article

Mixed H₂/H_∞ guaranteed cost control for high speed elevator active guide shoe with parametric uncertainties

¹ School of Mechanical and Electrical Engineering, Shandong Jianzhu University, Jinan City, PR China
² Shandong Fuji Zhiyu Elevator Co., Ltd, Dezhou City, PR China

^* e-mail: zhangruijun@sdjzu.edu.cn

Received: 5 January 2020
Accepted: 18 May 2020

Abstract

Aiming at the phenomenon that the elevator car system generates horizontal vibration due to the unevenness of the guide rail and the guide shoe modeling uncertainty caused by friction, wear and spring aging between the rolling guide shoe and the guide rail, a mixed H₂/H_∞ optimal guaranteed cost state feedback control strategy is proposed. Firstly, as the high-speed elevator car system always exist the phenomenon of stiffness and damping uncertainty in the guide shoe, the LFT method is adopted to construct the state space equation of the car system with parameter uncertainty. Secondly, considering the performance indexes of horizontal acceleration at the center of the car floor and the guide shoe vibration displacement system, an optimal guaranteed performance state feedback controller is designed based on the linear convex optimization method, which to minimize H₂ performance index and achieve the specified H_∞ performance level. Thirdly, the free matrix is introduced to reduce the conservatism of the controller. Finally, by comparing the simulation results with other control methods under the same conditions, it is verified that the control strategy can make the car system have better vibration suppression ability, and can significantly improve the ride comfort of the elevator.